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How to Add, Subtract, Multiply & Divide Polynomials

Adding/Subtracting Polynomials

When adding/subtracting polynomials, you need to group similar terms.
For example:


3a³-6a²+ 5a³+12a²= 8a³+6a²


12X² + X² = 13X²


4Y - 5Y= -1Y


17X² + 2X + 8X²+ 5X = 25X²+ 7X


Multiplying/Diving Polynomials:


When multiplying or dividing polynomials you need to use the rules of exponents.


For Example:


3X(X³+ 4X²) = 3X⁴+ 12X³


4Y⁴(Y²+ 6Y)= 4Y⁶+ 2



Foil Method


The foil (Fist, Outer, Inner, Last) method is used to multiplying two binomials


Let's say you need to multiply (X+1)(X-4) then you start with the first term: X(X)= X2


Then the second term: X(-4)= -4X


Then (1)(X)= X


and finally 1(-4)= -4


Now you get the final expression
(X+1)(X-4)= X²- 4X + X -4


Group common terms, in this case (-4X + X= -3X)


= X²- 3X - 4